Consider a section of muscle tissue of cylindrical shape with a radius of 1.5 cm. During highly rigorous exercise, metabolic processes generate 15 kW/m³of bulk tissue. The outer surface of the tissue is maintained at 37°C.

The thermal conductivity of the muscle tissue is k_m = 0.419 W/m · K.
a. Develop a mathematical model to predict the steady-state temperature distribution, T(r), in the tissue along the radial position r. What is the temperature of the tissue at a distance 0.75 cm from the surface?
b. Develop a mathematical model to predict the maximum temperature inside the muscle tissue. What is the maximum temperature?
c. If the length of the muscle, L, is 10 cm, what is the heat flux (W/cm²) leaving the muscle tissue, assuming end effects can be neglected?
d. Now consider that a sheath 0.25-cm thick surrounds the muscle tissue. This sheath has a thermal conductivity of 0.3 W/m · K and does not generate any heat. If the outer surface of this sheath is maintained at 37°C, what is the new maximum temperature within the muscle tissue?

Transcribed Image Text:

simplified cross section L[0.25 cm 0.419 W/m-K tissue 1.5 cm %3! Ts = 37°C 0.30 W/m-K sheath